Finite Group Databasebeta

← #16846215

Subgroups — #16846215

Order 3968.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521847C211yesmaximal, characteristic
2C4×#92495C211yesmaximal, characteristic, complemented
3#14521065C211yesmaximal, characteristic, complemented
4#14521023C211yesmaximal, characteristic, complemented
5#14520820C211yesmaximal, characteristic, complemented
6#14520809C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12#11758528—21no—
13#11758527—22no—
14#11758526—21no—
15#11758519C412yescomplemented
16#11758509C412yescomplemented
17C4×C22⋊D31—22no—
18#11758503C2211yescharacteristic
19#11758503C2211yescharacteristic
20C2×#92474C2211yescharacteristic
21C4×D124—21no—
22#11758449—21no—
23C42×D31—21no—
24C4×Dic62—21no—
25C31×#104—21no—
26C31×#104—21no—
27#11758422—22no—
28#11758413—22no—
29#41×C31—21no—
30#41×C31—21no—
31#41×C31—21no—
32#41×C31—21no—
33C2×Q8×C31C2×C411yescharacteristic, complemented
34C2×D4×C31—21no—
35C2×D4×C31C2×C411yescharacteristic, complemented
36C22×C4×C31—21no—
37C22×C4×C31—21no—
38C22×C4×C31C2311yescharacteristic
39C2×C22⋊D31—21no—
40#92495—21no—
41#92495—21no—
42#92495C2×C412yes—
43#92495D412yes—
44C2×D124D411yescharacteristic
45C2×C4×D31—21no—
46C2×C4×D31—22no—
47C2×Dic62D411yescharacteristic
48M16×C31—21no—
49M16×C31—21no—
50C2×C8×C31—21no—
51C42×C31—21no—
52C42×C31D411yescharacteristic
53C42×C31D411yescharacteristic
54C22⋊Dic31—21no—
55C22⋊Dic31D412yes—
56#92482—22no—
57#92481—22no—
58#92480—22no—
59#92479—22no—
60(C2×D31)⋊C4—22no—
61C4⋊Dic31—21no—
62C4⋊Dic31—21no—
63Dic31⋊C4—22no—
64C4×Dic31—22no—
65C4×Dic31—21no—
66C4×Dic31—21no—
67#92474—21no—
68#92474C2×C412yescomplemented
69C2×C31⋊C8—21no—
70C23×C31—21no—
71C23×C31C2×D411yescharacteristic
72C22×D31—21no—
73Q8×C31—21no—
74Q8×C31—21no—
75D4×C31—21no—
76D4×C31—21no—
77D4×C31—41no—
78D4×C31—41no—
79C2×C4×C31—21no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—42no—
83C2×C4×C31—41no—
84C2×C4×C31—41no—
85C2×C4×C31C22×C411yescharacteristic
86C2×C4×C31C2×D411yescharacteristic
87C2×C4×C31C2×D411yescharacteristic
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31#4111yescharacteristic
90C2×C4×C31#4111yescharacteristic
91C22⋊D31—22no—
92C22⋊D31—22no—
93C2×Dic31—21no—
94C2×Dic31—22no—
95C2×Dic31—41no—
96D124—21no—
97D124C22⋊C412yes—
98C4×D31—22no—
99C4×D31—22no—
100C4×D31—44no—
101Dic62—21no—
102Dic62C22⋊C412yes—
103C8×C31—41no—
104C31⋊C8—22no—
105#1906—311nomaximal, Sylow
106C22×C31—41no—
107C22×C31—41no—
108C22×C31—81no—
109C22×C31C4×D411yescharacteristic
110C22×C31#12011yescharacteristic
111C22×C31#12111yescharacteristic
112C2×D31—22no—
113C2×D31—42no—
114C4×C31—22no—
115C4×C31—41no—
116C4×C31—41no—
117C4×C31C2×C22⋊C411yescharacteristic
118C4×C31C4×D411yescharacteristic
119C4×C31#12111yescharacteristic
120C4×C31#12311yescharacteristic
121Dic31—22no—
122Dic31—42no—
123Dic31—81no—
124#575—311no—
125C4×#41—311no—
126#421—311no—
127C2×#104D3111yescharacteristic, complemented
128#410—311no—
129#344—311no—
130#339—311no—
131C2×C31—21no—
132C2×C31—21no—
133C2×C31—21no—
134C2×C31—81no—
135C2×C31#38611yescharacteristic
136D31—42no—
137C2×#41—311no—
138C2×#41C2×D3111yescharacteristic
139#137—312no—
140#137—621no—
141AGL(1,ℤ/8)—312no—
142AGL(1,ℤ/8)—621no—
143#135—622no—
144C2×M16—311no—
145C2×M16C2×D3111yescharacteristic
146C4×Q8—621no—
147C4×D4—621no—
148C4×D4—622no—
149#117—311no—
150#117—311no—
151#117—621no—
152C2×C42—621no—
153C2×C42C2×D3111yescharacteristic
154#104—21no—
155#104—21no—
156#104—622no—
157#99—622no—
158C31#190611yescharacteristic, complemented, Sylow
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—312no—
164#41—312no—
165#41—621no—
166#41—621no—
167C2×Q8—311no—
168C2×Q8C4×D3111yescharacteristic, complemented
169C2×D4—21no—
170C2×D4—311no—
171C2×D4—621no—
172C2×D4C4×D3111yescharacteristic, complemented
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—622no—
176C22×C4—621no—
177C22×C4C22×D3111yescharacteristic
178Q16—622no—
179SD16—622no—
180SD16—622no—
181D8—622no—
182M16—21no—
183M16—21no—
184M16—312no—
185M16—621no—
186C2×C8—21no—
187C2×C8—621no—
188C4⋊C4—622no—
189C4⋊C4—621no—
190C4⋊C4—621no—
191C22⋊C4—312no—
192C22⋊C4—622no—
193C22⋊C4—621no—
194C42—21no—
195C42—622no—
196C42—621no—
197C42—621no—
198C42C22⋊D3111yescharacteristic
199C42C22⋊D3111yescharacteristic
200C23—21no—
201C23—621no—
202C23D4×D3111yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—312no—
206Q8—621no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—312no—
212D4—622no—
213D4—622no—
214D4—621no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—621no—
222C2×C4—622no—
223C2×C4—622no—
224C2×C4—622no—
225C2×C4—1244no—
226C2×C4—1241no—
227C2×C4C2×C4×D3111yescharacteristic
228C2×C4#9249511yescharacteristic
229C2×C4D4×D3111yescharacteristic
230C2×C4D4×D3111yescharacteristic
231C2×C4#9249711yescharacteristic
232C2×C4C2×C22⋊D3111yescharacteristic
233C8—41no—
234C8—622no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—622no—
239C22—1242no—
240C22(C22⋊D31)⋊C411yescharacteristic
241C22#1175846111yescharacteristic
242C22#1175851411yescharacteristic
243C4—22no—
244C4—41no—
245C4—41no—
246C4—622no—
247C4—1242no—
248C4—2481no—
249C4C22⋊C4×D3111yescharacteristic
250C4#1175846011yescharacteristic
251C4C4×C22⋊D3111yescharacteristic
252C4#1175851511yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—81no—
257C2—1242no—
258C2#1452092511yescharacteristic
subgroupG/H
centerC4#11758515
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC2×C31#386
prime radical#14521847C2
cosocleC22×C4×C31C23
hypercenterC2×#104D31
hypocenterC31#1906
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×#92495C2semidirect
3. #14521065C2semidirect
4. #14521023C2semidirect
5. #14520820C2semidirect
6. #14520809C2semidirect
7. C2×C31×#104C2semidirect
15. #11758519C4semidirect
16. #11758509C4semidirect
33. C2×Q8×C31C2×C4semidirect
35. C2×D4×C31C2×C4semidirect
68. #92474C2×C4semidirect
127. C2×#104D31semidirect
158. C31#1906semidirect
168. C2×Q8C4×D31semidirect
172. C2×D4C4×D31semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145218472
C4×#924952
#145210652
#145210232
#145208202
#145208092
C2×C31×#1042
#190631